Slow oscillation‐spindle cross‐frequency coupling predicts overnight declarative memory consolidation in older adults

Cross‐frequency coupling (CFC) between brain oscillations during non‐rapid‐eye‐movement (NREM) sleep (e.g. slow oscillations [SO] and spindles) may be a neural mechanism of overnight memory consolidation. Declines in CFC across the lifespan might accompany coinciding memory problems with ageing. However, there are few reports of CFC changes during sleep after learning in older adults, controlling for baseline effects. Our objective was to examine NREM CFC in healthy older adults, with an emphasis on spindle activity and SOs from frontal electroencephalogram (EEG), during a learning night after a declarative learning task, as compared to a baseline night without learning. Twenty‐five older adults (M [SD] age = 69.12 [5.53] years; 64% female) completed a two‐night study, with a pre‐ and post‐sleep word‐pair associates task completed on the second night. SO‐spindle coupling strength and a measure of coupling phase distance from the SO up‐state were both examined for between‐night differences and associations with memory consolidation. Coupling strength and phase distance from the up‐state peak were both stable between nights. Change in coupling strength between nights was not associated with memory consolidation, but a shift in coupling phase towards (vs. away from) the up‐state peak after learning predicted better memory consolidation. Also, an exploratory interaction model suggested that associations between coupling phase closer to the up‐state peak and memory consolidation may be moderated by higher (vs. lower) coupling strength. This study supports a role for NREM CFC in sleep‐related memory consolidation in older adults.

Coupling strength and phase distance from the up-state peak were both stable between nights.Change in coupling strength between nights was not associated with memory consolidation, but a shift in coupling phase towards (vs.away from) the up-state peak after learning predicted better memory consolidation.Also, an exploratory interaction model suggested that associations between coupling phase closer to the up-state peak and memory consolidation may be moderated by higher (vs.lower) coupling strength.This study supports a role for NREM CFC in sleep-related memory consolidation in older adults.
K E Y W O R D S ageing, brain oscillations, cross-frequency coupling, overnight memory consolidation, sleep
Phase-amplitude CFC reflects the association or synchronisation between the phase of a slower oscillation and amplitude of a faster oscillation, and is typically quantified using measures of coupling strength and coupling phase.Measures of coupling strength (e.g.mean vector length, modulation index) reflect the extent of modulation in amplitude of a faster-frequency oscillation in relation to the up-and down-phase of a slowerfrequency oscillation (cf.Hülsemann et al., 2019).Measures of coupling phase reflect the average point in time (i.e.mean phase-angle direction in circular space from 0 to 360 ) on the slower oscillation where the faster oscillation amplitude is highest.
Several studies have demonstrated that fast spindle activity (e.g.12-16 Hz) in healthy adults tends to increase following the SO down-state and reaches its maximum amplitude or power often during or surrounding the depolarising SO up-state peak (e.g.Cox et al., 2014;Helfrich et al., 2018;Mölle et al., 2002Mölle et al., , 2011;;Niknazar et al., 2015).By contrast, slower spindles (e.g.9-13 Hz) often reach a maximum peak during the SO up-to-down-state transition and towards the down-state peak (e.g.Mölle et al., 2011;Muehlroth et al., 2019;Yordanova et al., 2017).Slowoscillation-to-sigma CFC (SO -σ CFC) is one part of a larger process of coordinated neural activity that occurs between cardinal NREM oscillations.Chiefly, as cortical SOs group TC spindles, the 'trough' phase of spindle oscillations in turn group hippocampal (HC) ripple activity (Clemens et al., 2007;Staresina et al., 2015;Sullivan et al., 2015).This triple phase locking of SO, spindle, and ripple activity is argued as a mechanism to support a HC-neocortical dialogue during NREM sleep, in line with the active systems consolidation model of sleep-dependent memory processes (e.g.Ackermann & Rasch, 2014;Cairney et al., 2015;Todorova & Zugaro, 2020).
The hypothesis that SO -σ CFC facilitates memory is supported by experimental work; however, this specific area of research is still in early phases, as only a relative minority of studies to examine CFC during sleep did so in the context of memory.There are a number of studies to date which have demonstrated that overnight memory consolidation is positively associated with fast spindle (e.g.12-15 Hz) activity coupled with the SO up-state peak (e.g.Bar et al., 2020;Ladenbauer et al., 2017;Mikutta et al., 2019;Muehlroth et al., 2019;Ngo et al., 2013;Niknazar et al., 2015;Schreiner et al., 2021).Conversely, fewer studies have examined relations between learning/ memory and SO coupling with slow spindle activity: One study reported inconsistent increases in slow spindle activity after a word-pair learning task (Mölle et al., 2011), another reported that greater CFC with slow (vs.fast) spindle activity near the up-state in young adults is associated with worse scene-word memory (Muehlroth et al., 2019), and a third study reported that more slow spindle power in time with an SO (i.e.up-to-down-state transition) was associated with lower response latency on a (spatial navigation) memory task (Bastian et al., 2022).
Most available studies of CFC and memory include samples of healthy young adults (e.g.Bar et al., 2020;Bastian et al., 2022;Cairney et al., 2018;Dehnavi et al., 2021;Denis et al., 2021;Mikutta et al., 2019;Mölle et al., 2004Mölle et al., , 2009Mölle et al., , 2011;;Niknazar et al., 2015;Perrault et al., 2019;Ruch et al., 2012;Yordanova et al., 2017;Zhang et al., 2020).However, there is a general paucity of studies that examine CFC and memory among more middle-aged (Bartsch et al., 2019;Demanuele et al., 2017;Mylonas et al., 2020;Schneider et al., 2020) and older adult participants (Helfrich et al., 2018;Ladenbauer et al., 2017Ladenbauer et al., , 2021;;Muehlroth et al., 2019).Both SOs and spindles are NREM oscillations whose activity (e.g.density, amplitude) declines with older age (e.g.Carrier et al., 2011;Martin et al., 2013), and there is some evidence that the same is true for SO -σ CFC.Schneider et al. (2020) demonstrated that memoryassociated benefits of SO-timed auditory stimulation, and related coupling response, were weaker in middle-aged adults relative to a young adult dataset.Two recent studies (Helfrich et al., 2018;Muehlroth et al., 2019) both demonstrate that fast spindle activity peaks earlier in the SO rising phase in healthy older versus younger adults, and that SO -σ de-coupling in older age is associated with reduced grey matter volume in the medial prefrontal cortex (mPFC), as well as worse performance on tests of declarative memory.A fourth study in older adults with mild cognitive impairment (Ladenbauer et al., 2017) demonstrated that transcranial direct current stimulation applied during post-learning N2 sleep enhanced fast spindle coupling with the SO up-state versus a sham condition, and a stronger SO-spindle synchronisation index in the stimulation condition was associated with better visual recognition memory.
Together, there is some early evidence for ageingrelated changes in SO -σ CFC during sleep, and that weak or poor synchronisation between SO and spindle activity in older adults may help explain memory impairments that coincide with ageing.However, relatively less is known about relations between SO -σ CFC and memory in the context of lifespan ageing.Also, of the available studies of SO -σ CFC and learning/memory, many of them rely on or showcase data from only one sleep recording visit (e.g.Bar et al., 2020;Cairney et al., 2018;Cross et al., 2021;Helfrich et al., 2018;Mikutta et al., 2019;Muehlroth et al., 2019).Such absence of a baseline control night limits inferences about whether SO -σ CFC is more of a state-dependent oscillatory phenomenon that can be manipulated by pre-sleep experience or a stable, trait-like activity that reflects general cognitive abilities.
Given the current state of knowledge about SO -σ CFC and memory above, the current study had two specific major aims: First, we examined whether learning a declarative memory task changes SO -σ CFC during subsequent sleep in healthy older adults.For this, we hypothesised that SO -σ coupling strength would be increased, and the corresponding coupling phase would be closer to the SO up-state, during sleep after a declarative learning task versus a baseline night with no task.Second, we examined whether SO -σ CFC during sleep between nights (i.e. after learning vs. before) is related to performance on the sleep-dependent declarative memory task.For this, we hypothesised that stronger coupling strength and coupling phase closer to the SO up-state after completing the learning task will be associated with better overnight memory consolidation.Following these two major aims, we also conducted an exploratory examination to see if a more complex dynamic in predicting memory consolidation is revealed when we consider a statistical interaction between the two measures of coupling strength and coupling phase measured after a presleep learning period (e.g. if one moderates the other).

| Participants and recruitment procedure
Healthy older adults were recruited from the general Montréal community.Participants were recruited using a two-stage evaluation, involving (1) a brief, telephonebased screening interview, and (2) an in-person assessment of sleep and general health, and to screen cognitive functioning.The in-person interview assessed sleep (e.g.regularity, quality), health (e.g.medication, medical history), physical activity (e.g.weekly exercise) and daily habits (e.g.caffeine use and alcohol).The participants also completed the Mini Mental State Exam (MMSE; Crum et al., 1993;Magni et al., 1996;Tombaugh & McIntyre, 1992) and Montreal Cognitive Assessment (MoCA; Nasreddine et al., 2005;Rossetti et al., 2011), and a battery of questionnaires.
Older adults (55-85 years-old) were eligible for this study if they satisfied the following a priori criteria: no chronic/unstable medical condition (e.g.infection, acute and severe medical event, uncontrolled diabetes); not having a sleep disorder (e.g.chronic insomnia [sleep difficulty > three nights per week for > 3 months], severe sleep apnea [defined by AHI ≥ 30/hr], parasomnia); no excessive alcohol use (i.e.drinks ≤ 10 glasses/week) or use of illicit drugs (including cannabis > 1 time per month); not currently working night shifts and/or has not travelled through more than one time zone during the last 6 weeks; no history of brain hemorrhage, tumour, or any condition that required brain surgery; no major psychiatric (e.g.psychosis and mood disorder) or neurological disorders/acute neurological disease (< 1 yr; e.g.stroke and epilepsy); and not currently using a hypnotic or any other psychotropic medication on a regular basis, and no medications that otherwise impact alertness or sleep.Older adults were excluded if they scored < 27 on the MMSE and/or < 24 on the MoCA.Volunteers were also excluded if they surpassed threshold scores on two or more screening questionnaires based on the following criteria: Insomnia Severity Index (≥ 15; Bastien et al., 2001;Morin et al., 2011); Pittsburgh Sleep Quality Index (≥ 5; Buysse et al., 1991); Epworth Sleepiness Scale (≥ 10; Johns, 1991Johns, , 1992)); Stop-BANG sleep apnea screening questionnaire (≥ 5; Boynton et al., 2013;Silva et al., 2011); Horne-Östberg Morningness-Eveningness Questionnaire (≤ 30, 'Very Evening' types; Horne & Östberg, 1976;Taillard et al., 2004); Geriatric Depression Scale (≥ 15; Yesavage et al., 1982); and Geriatric Anxiety Inventory (≥ 10; Pachana et al., 2007).
A total of 43 older adults were deemed eligible after the interview and scheduled for their first recording night, used to rule out the presence of sleep disorders, primarily severe sleep apnea, and to act as a baseline.The participants with mild or moderate sleep apnea were retained to not impose overly strict criteria for older adults that could limit the generalisability of our study.Six of the original 43 participants were excluded after Night 1 because of severe sleep apnea or otherwise abnormal sleep, and a seventh participant withdrew.The remaining 36 eligible participants completed a second visit (learning/memory task night) at least 1 week later.Among these, 11 were later excluded (n = 1 for technical/recording problems, n = 6 for poor sleep efficiency [< 70%] on one or both nights, n = 4 for poor testing performance [pre-sleep recall score < 10]).In our aim to examine learning and overnight memory consolidation in cognitively healthy older adults, we chose to exclude participants who evidenced especially poor initial encoding and retention of our word-pair stimuli, and thus had limited information available to consolidate during overnight sleep.The final sample was comprised of 25 participants.

| Study protocol
The study protocol is displayed in Figure 1.The participants were scheduled to arrive at the lab on both nights between 7:00 PM and 9:00 PM, adjusted for individual schedules.Both overnight sleep recordings included standard polysomnography (PSG) recordings (see below) that took place in a private bedroom in our sleep laboratory.The participants were instructed to abstain from drinking alcohol or excessive caffeine in the 24 hrs before each visit.Upon arriving for their Night 1 visit, the participants were given instructions for completing a daily sleep diary and for using a wrist actigraphy device (Actiwatch) to be worn daily until their second visit.The participants returned at least 7 days later to complete their Night 2 visit, which proceeded after verifying that their sleep patterns in the last week were stable/regular and typical for each person across the study interval between sleep recordings.
The second recording visit included a pre-and postsleep word-pair associates memory task, completed after the equipment set-up (see below).The participants were tested on the word-pair task in either French or English, depending on which language they learned first and were most comfortable using in daily life.Immediately after the word-pair task learning period (described below), the participants completed a pre-sleep recall task (PM recall) and were then free to go to bed according to their reported usual bedtimes.The next morning, the participants were offered a light breakfast and, when ready, began the post-sleep cued-recall test (AM recall).AM recall testing began an average (SD) of 29.04 (13.39) min after Lights On.Following the AM test, the participants completed two additional cognitive tasks: an N-back and a Go/no-go task; data from these additional tasks are not reported here, as the primary focus of this study is on SO-sigma (SO -σ) CFC and relations with overnight declarative memory consolidation.After finishing all three morning tasks, the participants were disconnected from the recording equipment and offered shower facilities and monetary compensation.All study procedures and documents were approved by designated ethics committees at both Concordia University and the Centre de recherche de l'Institut universitaire de gériatrie de Montréal (CRIUGM), and all volunteers provided written consent before participating.
Hereafter, the first (Night 1) recording is referred to as the 'baseline' visit, whereas the second (Night 2) recording is referred to as the 'learning' visit.

| Cognitive testing: Word-pair associates
The primary task used in this study is a variant of the word-pair associates task (Backhaus et al., 2007;Plihal & Born, 1997).This task was chosen to maintain consistency with other related studies (e.g.Mölle et al., 2004Mölle et al., , 2009Mölle et al., , 2011;;Zhang et al., 2020), and because it is designed as a task of HC-dependent associative memory.The task we designed included 40 pairs of nouns with minimal semantic similarity.Nouns were of standardised length (5-9 characters), word-frequency (> 5 per million; e.g.Corpus of Contemporary American English [for English words]; Lexique 3, http://www.lexique.org/[for French words]) and emotionality (within a broadly neutral range; Bradley & Lang, 1999;Warriner et al., 2013).Equivalent lists were developed in both English and French, balanced to match the words used in each list as closely as possible.Before starting the task, the participants were shown instructions on-screen and given additional verbal explanation.Word-pairs were presented on a computer screen as vertically stacked and in large-text font.A blank screen followed each presentation, and a centred fixation cross indicated the next word-pair is coming up.During the blank screen, the participants were instructed to form a visual mental image of the two words just presented, as a strategy to facilitate the forming of word associations.Word-pair stimuli were presented in two learning trials.During the first learning trial, stimulus presentation was 5 sec, followed by a 5-sec blank screen, and a 5-sec fixation cross to indicate that the next pair is coming up.During the second learning trial, stimulus presentation was 3 sec long, followed by a 3-sec blank screen and a 5-sec fixation cross.Word-pairs were arranged randomly between the first and the second learning trials to reduce primacy and recency effects.Each learning trial was followed by a 2-min break period.Including instructions and rest periods, duration of the learning trial was approximately 25 min.
After all word-pairs were presented twice, and after the second 2-min break, the participants underwent a short-delay cued-recall test (PM recall), where they were shown the first word in a pair on the screen and asked to recall the second word verbally.A research assistant scored verbal responses.The participants pressed a keyboard button after each response to proceed to the next trial, allowing for an unrestricted recall time.The postsleep (AM recall) test consisted only of the cued-recall procedure and was identical to the pre-sleep test, except that word-pair cues were randomised again.No feedback was given to the participants after responding on either test.The primary outcome variable was a measure of overnight memory consolidation, calculated as the number of correct word-pair responses involving the same word pairs during both PM and AM recall tests.This approach is consistent with previous studies of sleep and memory examining the overnight 'maintenance' of remembered items (e.g.Dumay, 2016;Muehlroth, Sander, et al., 2020).

| Overnight sleep recordings
The first overnight sleep recording consisted of a full PSG set-up, with electroencephalogram (EEG), electrooculogram (EOG), electromyogram (EMG), and electrocardiogram (ECG) sensors, a transcutaneous finger pulse oximeter (SpO2), and measures of respiration (oral-nasal thermocouple and nasal pressure cannula, thoracic and abdominal piezo-electric belts), and leg movements (leg F I G U R E 1 Schematic of the study design.Participants deemed eligible after the in-person interview underwent a first night of polysomnography (PSG) screening.If no major sleep disorder was detected (e.g.severe sleep apnea), the participants returned at least 7 days later for a learning task night (word-pair associate's task).The participants completed daily sleep diary entries and were monitored by wrist actigraphy between the two recording visits.In the learning task, the participants were shown a list of 40 word pairs, with two list presentations during encoding.Encoding was followed by a pre-sleep (PM; short-delay) cued recall test, where the first word was displayed and the participants had to recall the associated word.Verbal responses were recorded by a research assistant.The next morning after overnight sleep, the participants completed a post-sleep (AM; long-delay) cued recall test.
EMG).The PSG electrode montage included 12 channels, positioned according to the American Academy of Sleep Medicine (AASM) International 10-20 placement system (Fz, F3, F4, Cz, C3, C4, O1, O2, M1, M2, Pz reference, Fpz Ground).The first (PSG) visit provided a baseline measure of brain activity during sleep.Respiratory and SpO2 monitoring alongside EEG during the first recording night allowed for screening and exclusion of older adults with severe sleep apnea.

| EEG analysis
Sleep records were scored for different sleep stages using Domino software, and subsequently processed using an open-source Python software package ('Wonambi'; https://github.com/wonambi-python/wonambi),developed in-house.Sleep EEG data were visually scored in 30-s epochs in one of four stages of sleep (N1, N2, N3, REM) by an experienced sleep scorer according to standard criteria (e.g.Iber et al., 2007) and with consideration of smaller slow wave amplitude in older adults when scoring N2 and N3 (Webb & Dreblow, 1982).Sleep cycles were identified as periods of sleep containing at least 15 min of NREM sleep and 5 min of REM sleep, except for the first sleep cycle, which could contain > 0 min of REM (Feinberg & Floyd, 1979).An exception was made when there was no identifiable period of REM sleep occurring in the first sleep cycle; in this rare case, the cycle end was marked during a clear period of wakefulness or prominent arousal from sleep that occurred between around 90 and 120 min after stable sleep onset.
EEG sleep recordings for each participant on both study nights were reviewed in 30-s epochs to identify artefacts or otherwise poor/interrupted signal and tag them for exclusion from later analysis.A secondary pass using 15-s epochs was performed, if necessary, to reduce uncertainty when present.Signal aberrations targeted for removal included poor/dysfunctional signal > 1 sec (e.g.signal popping and flat lining), excessive muscle artefact or movement, micro-arousal activity (e.g.sudden burst of sustained [> 3 sec] faster-frequency activity, usually associated with elevated chin EMG), or periods in an epoch that contained a shift to N1 or wakefulness.

| SO and spindle detection
Automatic detection of SO and spindle events was performed using Wonambi, applying previously validated detection algorithms.SOs were detected using an algorithm described by Staresina et al. (2015).SOs were detected from separate N2 and N3 sleep stages using artefact-free EEG data filtered between .16 and 1.25 Hz (zero-phase infinite impulse response [IIR] bandpass filter).Next, candidate SO waves were identified based on zero crossings in the filtered signals (down-states followed by up-states), as well as event duration and amplitude criteria.Event duration was defined as the time between two successive positive-to-negative zero crossings, limited to within .8-2sec.Event amplitude (troughto-peak amplitude between two positive-to-negative zero crossings) was determined individually, based on amplitudes that exceeded the 75th percentile of candidate amplitudes for that participant.The resulting SO detection fell within a bandwidth of .5-1.25 Hz.
Spindle detection (based on Mölle et al., 2011) was performed using artefact-free EEG data in separate N2 and N3 sleep stages.Spindles were detected using a fixed bandwidth in the slow spindle range on Fz (9-13 Hz) and in the fast spindle range on Cz (12-16 Hz), given the frontal and central predominance of slow and fast spindles, respectively (Cox et al., 2017;Fernandez & Lüthi, 2020;Werth et al., 1997).After band-pass filtering artefact-free data within each frequency band, the root-mean-square (RMS) of the filtered signal was calculated at each data point using a .2-secsliding window and subsequently smoothed with additional filtering.RMS values exceeding thresholds by 1.5 SD for between .5 and 3 sec were identified as spindles.

| Event-locked CFC
SO -σ phase-amplitude CFC during the total NREM (N2 + N3) period was analysed using SOs detected from N2 and N3 sleep stages, following concatenation.We combined the N2 and N3 detections to account for the occurrence of SOs in both sleep stages (e.g.Malerba et al., 2018;Menicucci et al., 2009).Coupling analyses performed on detected EEG events minimise detection of spurious coupling in the data by ensuring a rise in power in the phasegiving frequency range (c.f.Aru et al., 2015).Specialised analysis scripts constructed phase-amplitude distributions on each detected SO event, and from these data, we calculated the Modulation Index (MI; Tort et al., 2010) and measures of preferred coupling phase.Primary analyses focussed on SO -σ CFC from frontal (Fz) EEG data across both study nights, given the frontal predominance of SO (Bersagliere et al., 2018;Massimini et al., 2004).The 9-13 Hz fixed frequency band we used is largely consistent with previous examinations of spindle frequency characteristics (e.g.Cox et al., 2017;Ujma et al., 2015) and studies of SO -σ CFC on frontal channels (e.g.Klinzing et al., 2016;Ladenbauer et al., 2017;Muehlroth et al., 2019;Yordanova et al., 2017).Analyses on Cz data (12-16 Hz) are reported in the supporting information.
The MI (Tort et al., 2010) is an information-theoretic metric based on the Kullback-Leibler distance function, which allows a model-free quantification of the divergence between two statistical distributions.Empirical distributions obtained from the phase-amplitude data are compared using a Shannon entropy approach with a template distribution that assumes no coupling effects, depicted by a flat/uniform distribution (Hülsemann et al., 2019).The MI ranges from 0 to 1, with larger values reflecting greater coupling strength between two oscillation frequencies.For each participant on each study night, SO -σ MI was calculated from detected SO events across the whole night.Each event was filtered using a Hilbert transform in two ways: first, in the SO frequency band to extract the instantaneous phase time series, and second, in the sigma frequency band to extract the instantaneous amplitude time series.A 2-sec buffer was included on either side of the signal for each SO event to avoid filter edge artefacts; the buffer was discarded after filtering.Each filtered event was then binned (18 bins), and the amplitude in each bin was averaged across all events into a single, grand average phase-amplitude time series which was submitted for MI analysis.Raw MI values were log-transformed to better capture harmonic proportions of neural oscillatory activity across lower to higher frequencies (cf. Buzs aki & Draguhn, 2004;Penttonen & Buzs aki, 2003) and to improve normality within the data.As a result of this transformation, given that raw MI is a value from 0 to 1, greater log-transformed MI is indicated by a value that is less (vs.more) negative, with a lower limit of -∞ and an upper limit of 0.
Preferred coupling phase was quantified from this same grand average phase-amplitude time series by extracting a measure of circular mean direction to reflect the preferred SO phase (in radians) of maximum sigma power amplitude.Like the MI, a single value was produced for each participant on each night.We arranged our coupling phase analysis such that the depolarising SO up-state was positioned on the circular/polar plot at 270 , and the hyperpolarising SO down-state was positioned at 90 (See Figure 2c).Rather than using the raw coupling phase values, our analysis instead focused on a transformed value of coupling phase distance from the SO up-state.This variable, used in our linear regression models to predict memory consolidation scores (see below), was derived using the following steps.First, each participant's raw coupling phase value (on a scale of 0-360 ) was subtracted from a common reference point of 270 (i.e. the up-state).Second, resulting values were then re-scaled by subtracting 360 from difference scores > + 180 and adding 360 to difference scores > À 180 , which placed all scores on a range from À180 to +180 , now reflecting a distance either before or after the upstate.Because of outliers and poor distributional qualities (e.g.skewness), the absolute value of this score was then taken, whereby larger values reflect a distance further away from the up-state peak but do not indicate in which direction (before vs. after).Hereafter, this transformed absolute coupling phase distance variable is referred to simply as CP.This measure is similar to one used in a study of SO-spindle CFC and memory in children and youth (Hahn et al., 2020); however, the measure derived from their method reflected the proportion of spindles (among all spindles) that occurred within a specific range around the SO up-state peak.
Measures of MI and CP, derived during a combined N2 + N3 stage of all-night sleep, were compared between baseline and learning nights to examine any significant changes after completing the word-pair task.Coupling measures were then examined for associations with memory consolidation, using relative change in MI and CP between the two nights, calculated as [(learning night) À (baseline night)] and referred to as relative MI (rel_MI) or relative CP (rel_CP).In turn, rel_MI reflects an increase or decrease in coupling strength between nights, and rel_CP reflects a shift in distance from the SO up-state between nights (i.e.closer to or further from the up-state).These same examinations of CFC between nights and in association with memory were also performed for data from stage N2 and N3 sleep considered separately (see supporting information Results).

| Data screening
Data for the primary demographic, cognitive testing and CFC (MI, rel_MI, CP, rel_CP) measures of interest were screened for univariate outliers, and adherence to statistical assumptions of normality, homogeneity of variance, and linear relationships.Univariate outliers were screened by visual inspection of box plots and formally identified by inspecting z-score frequency tables for values ±3 SD from the mean.Normality was examined using measures of skewness and kurtosis, using a Shapiro-Wilks test, and by visual inspection of histograms, Q-Q plots and box-plots.Normality of the deviation scores (X À mean) of each variable was also examined using similar methods.Homogeneity of variance was examined using Levene's test for each repeated-measure variable pair.Linearity was examined by inspecting bivariate scatterplots between primary predictor and outcome variables.
There were no univariate outliers across any of the main demographic, cognitive testing and CFC variables on either night.A positive skew and significant Shapiro-Wilks test (p = .003)in the apnea-hypopnea index (AHI) covariate are unsurprising given that most participants had an AHI < 10; this was corrected with a Log10 transformation.Homogeneity of variance was confirmed using a Levene's test with each pair of repeated-measures variables (MI and CP).Conversely, two outliers were found in our variable reflecting relative change in MI (rel_MI); a consensus was reached to remove data points identified as outliers and conduct analyses with these variables using a trimmed sample (n = 23 or 24), which improved this variable's distributional qualities (i.e.skewness and normality).Supplemental CFC variables were similarly screened, and outliers were also removed; however, most of the Czmeasured variables (rel_MI, CP, rel_CP) displayed skewness and non-normality that was only partially improved after removing outliers.The pattern of results was largely similar among analyses with the full sample.

| Between-night comparisons
To address our first study aim, we tested for betweennight differences in SO -σ CFC using a one-way, withinsubjects analysis of covariance (ANCOVA).Differences between nights in MI and CP were examined separately.Recording night (baseline vs. learning) was a repeatedmeasures factor.Age was included as a covariate, as well as AHI (measured on the baseline night, log-transformed), to account for added variability because of sleep apnea severity.Post-hoc t-tests were examined following a significant main effect or interaction.We also quantified the stability of MI between experimental nights using Pearson's correlations.

| Associations between MI and CP with word-pair memory
To address our second study aim, associations between CFC and memory were tested using hierarchical multiple regression, with age and log-AHI included in Step 1, and the CFC measure of interest in Step 2. The CFC model predictor we used was a difference score (learning night À baseline night) reflecting the relative (individual) change between study nights in measures of MI and CP.Each measure was entered in separate regression models to examine whether change in coupling strength or coupling phase distance from the up-state can predict overnight memory consolidation scores.The R 2 -change and F-scores of the model were examined alongside regression coefficients to determine the effects of each CFC variable in predicting word-pair performance.Absence of multicollinearity among predictors was also verified during data screening.

| Exploratory analysis: MI Â CP interaction
Lastly, we conducted an exploratory analysis to examine potential interaction or moderation effects between SO -σ MI and CP in predicting memory scores.To accomplish this, MI, CP and their interaction were each entered in a hierarchical regression model.The interaction was created by deriving the product of the mean-centred MI and meancentred CP values.In contrast to our main analyses above, which examined measures of relative change in coupling between nights, our exploratory interaction model focussed on CFC data measured from the learning night only.The MI-by-CP product term was entered in a regression model like those described above, with age and AHI entered at Step 1.At Step 2, the mean-centred main effect variables (MI and CP) plus the interaction (product) term were added to the model, and we examined R 2 -change and F-scores alongside regression coefficients.On detecting a statistically significant interaction, follow-up analyses examined the simple slopes of regression weights for the predictor variable (CP) at different levels of MI, which was treated as the moderator variable.For this step, two followup analyses were performed using the same regression approach, guided by the steps outlined by Meyers et al. (2013): The first follow-up analysis repeated the base interaction model after the centred MI variable was re-centred to reduce all values by 1 SD unit ('Low MI'), and the second follow-up repeated the base interaction model after the centred MI variable was re-centred to increase all values by 1 SD unit ('High MI').Follow-up analyses determined if the relationship between CP and memory consolidation changes with higher or lower coupling strength.

| Correction for multiple comparisons
A Bonferroni method was used to adjust our critical p-value to account for the number of analyses being performed using our primary independent measures.Each CFC variable (MI and CP) in our primary analyses on Fz was examined for between-night differences and associations with word-pair memory consolidation.In turn, four primary analyses were conducted, resulting in an adjusted p-value of (.05/4 = .0125= .013).Our exploratory analyses were evaluated with a more liberal criterion of p < .05.

| Sample characteristics and at-home screening
The participant demographics and eligibility screening results are presented in Table 1.The participants (M [SD] age = 69.12[5.53]) were modestly balanced in terms of sex (64% female) and were mostly French-speaking (80%) and right handed (80%).Years of education ranged from 12 to 26 (M [SD] = 16.78 [3.50]) yr.The participants maintained overall good-quality sleep between study nights, as reflected by the average sleep efficiency from their daily sleep diary (M = 84.36%)and wrist actigraphy (M = 77.88%).

| Behavioural data
The participants completed pre-sleep (PM) and post-sleep (AM) cognitive testing on their second recording visit.On the 40-item word-pair memory task, the participants recalled an average of 28.12 (SD = 7.12; range = 13-38) correct word-pairs on the PM cued-recall test, and an average of 26.16 (SD = 7.76; range = 11-39) correct word-pairs on the AM cued-recall test.The overnight (pre-sleep to post-sleep) absolute change in recall performance ranged from forgetting six word pairs to remembering an additional three (M [SD] = À1.96[2.44]; Med = À2; Mode = À1).The difference in performance between PM and AM recall tests was statistically significant (t(24) = À4.015,p = .001).The Overnight Consolidation score, reflecting the total number of correct wordpair responses involving the same word pairs between PM and AM recall tests, ranged from 9 to 38 across the sample (M [SD] = 24.88(7.93)).

| Sleep architecture
Table 2 presents sleep architecture and other basic sleep parameters from the first (baseline) and second (learning) study nights.The participants achieved slightly higher sleep efficiency (t(24) = À2.472,p = .021)on the learning night versus baseline.

| Discrete SO and spindle events
Presented in Table 3 are descriptive statistics and simple between-night comparisons of event-detected SOs and sleep spindles from Fz during all-night N2 + N3 sleep.There was a general trend for SO and sleep spindle activity to either remain stable or to decline (spindle peak-topeak amplitude) between baseline and learning nights.strength was not statistically different between nights (F [1, 22] = 3.252, p = .085).Similarly, CP did not significantly differ between nights (F [1, 22] = 3.784, p = .065).

| Specific aim 2: SO -σ CFC and overnight memory consolidation
As presented in Table 5 and Figure 3a, regression models indicate that rel_MI was not significantly associated with memory performance in this sample.However, a greater relative decrease in our transformed CP variable (reflecting a shift in coupling phase towards the up-state) was predictive of better memory consolidation (F [3, 21] = 5.732, ΔR 2 = .278,p = .005;B [SE] = À.108 [.033], β = À.569) (Table 5 and Figure 3b).

| Exploratory aim: interactions between MI and CP and relations with memory
Results from our exploratory interaction models are presented in Table 6.A model containing SO -σ MI, CP and their interaction significantly predicted memory consolidation scores (F [5, 19] = 4.399, ΔR 2 = .362,p = .008).
In the model itself, significant associations with memory were found for both the MI Â CP interaction (B [SE] = À.043 (.019), β = À.384, p = .033)and for the CP main effect (B [SE] = À.102 (.031), β = À.680, p = .004).Inspection of partial correlations suggests that the correlation with memory was strongest for CP (r = À.596).Follow-up analyses repeated the regressions with MI recentred to reduce values by 1 SD unit, and again with MI re-centred to inflate values by 1 SD unit.Follow-up analyses revealed that CP closer to the SO up-state remained a significant predictor of memory alongside the interaction when MI was shifted upward (i.e.reflecting greater coupling strength; β = À.978, p = .001)but was no longer a significant predictor after MI was shifted downward (i.e.reflecting less coupling strength; β = .381,p = .120).Inspection of partial correlations when the MI moderator was higher suggested that the association between memory and CP was even stronger than in the base model (r = À.654).See Figure 4 for a plot showing the simple slopes of these moderator analyses.In summary, MI remained stable between recording nights, and the individual (relative) change in coupling strength was not predictive of memory.Similarly, our measure of absolute distance in coupling phase from the SO up-state remained stable between nights, although a relative shift in CP towards the up-state after the learning task predicted better overnight memory consolidation.However, based on our examination of interactions between the two, our results suggested that the predictive effects of a coupling phase closer to the up-state peak are enhanced when accompanied by higher (vs.lower) coupling strength.

| DISCUSSION
The aim of this study was to examine CFC during NREM sleep and its association with learning and memory consolidation in healthy older adults, with a focus on phase-amplitude coupling between SO and slow spindle (sigma) activity (9-13 Hz) on the frontal midline (Fz).Our first main hypothesis that SO -σ CFC would increase from the baseline after the participants complete a pre-sleep learning task was not supported, as there was no difference between baseline and learning nights in our measure of MI or in our transformed measure of absolute coupling phase distance from the SO up-state (CP).Our second hypothesis that greater MI is positively associated with memory was not supported, although our hypothesis that a coupling phase closer to the SO up-state is associated with memory was supported.Specifically, using multiple regression, our data suggest that a relative shift from the baseline in coupling phase towards (vs.away from) the SO up-state after learning is predictive of better memory consolidation.Together, our measures of coupling strength and phase distance from the up-state were not affected on the group level by a pre-sleep learning experience; however, individuals whose coupling phase shifted closer to the up-state after learning appeared to retain more word pairs after overnight sleep.Lastly, an exploratory interaction model between MI and CP during post-learning sleep suggested that the association between a coupling phase closer to the up-state and better memory consolidation is facilitated or blunted by higher versus lower coupling strength, respectively.

| Current state of the literature: a comment on research standardisation
Compounding evidence from multiple correlational and experimental studies (mostly with young adults) has contributed ample support for the idea that more precise SO-spindle CFC is associated with better sleep-associated memory consolidation.However, there are noticeable differences in experimental and analytic methods across these studies that are important to consider when reviewing the currently available data.We highlight and discuss a selection of these differences below.
Most available studies of CFC and memory report data from overnight sleep, whereas some studies report data from a daytime nap (Bar et al., 2020;Ladenbauer et al., 2017Ladenbauer et al., , 2021;;Ruch et al., 2012;Schreiner et al., 2021) F I G U R E 2 Schematic representation of coupling dynamics.(a) Phase-amplitude histograms for Night 1/baseline (blue) and Night 2/learning (red) conditions.Each vertical bar reflects the sigma power mean amplitude (μV; y-axis) across each of the 18 Â 20 phase bins (xaxis).Error bars are for the standard error of the mean.Plotted below the histogram is a reference for the oscillation phase across the 18 bins; the hyperpolarising SO down-state is pointing down and is followed by the depolarising up-state, pointing up.Overall, slower sigma power amplitude peaked more in the up-to-down-state transition and was at its lowest shortly before the up-state.(b) Scatterplot displaying correlation for SO -σ modulation index (MI) between the baseline night (x-axis) and learning night (y-axis).The dashed line indicates equality from one night to the next.Correlation analysis suggests that SO -σ MI might be a stable, individual (trait-like) property in older adults.(c) Preferred (raw) coupling phase polar plots for Night 1/baseline (blue) and Night 2/learning (red).Each coloured bar represents the number of participants with the same overall coupling phase.The count scale (pointing to 130 on the circle) is reflected by the concentric rings extending from the centre of each circular figure.The orange line reflects the average coupling phase of the group on each night.The depolarising SO up-state corresponds to 270 on the circle (6:00 position) and the hyperpolarising down-state corresponds to 90 on the circle (12:00 position), with the phase-angle direction moving counter-clockwise.Consistent with Figure 2a, slower frontal spindle power tended to peak after the up-state phase.Next to Figure 2c is a graphical legend of SO phase angle and its relationship with the polar plots, with an example phase in orange (adapted from Ong et al., 2016).
or from an evening nap (Göldi et al., 2019).Given the known circadian factors that influence both sleep regulation (e.g.Borbély & Achermann, 1999;Dijk & Lockley, 2002) and brain oscillation activity (e.g.B odizs et al., 2022;Schalkwijk et al., 2019), studies of NREM SO -σ CFC from overnight sleep may not be equivalent to studies of SO -σ CFC from a daytime nap.Further, there is wide variability in the memory task studies employ.Broad distinctions can be drawn between studies of only declarative/episodic (e.g.Helfrich et al., 2018;Niknazar et al., 2015) or procedural memory (e.g.Bartsch et al., 2019;Cox et al., 2018) and studies that examine both (e.g.Ladenbauer et al., 2017;Mikutta et al., 2019).More fine-tuned differences include the type of training (e.g.1-2 list exposures or practice rounds [e.g.Mölle et al., 2009;Ngo et al., 2013] vs. learning to a criterion [e.g.Bar et al., 2020;Helfrich et al., 2018;Zhang et al., 2020]), and the type of memory being tested (e.g.emphasis on recognition [such as old vs. new; e.g.Cairney et al., 2018;Helfrich et al., 2018] vs. cued recall [e.g.Ngo et al., 2013;Schreiner et al., 2018] vs. a mix of both [Muehlroth et al., 2019]).The number of test items (i.e.single words, word pairs, word-nonsense word pairs, scene-image pairs) also varies.For example, studies  of declarative memory have used tasks with 15 (Mikutta et al., 2019), 40 (e.g. Ladenbauer et al., 2017) and 120 + test items (e.g.Mölle et al., 2011;Ngo et al., 2013).A study of ageing (Muehlroth et al., 2019) exposed seniors to fewer memory items on a scene-word memory task, as well as an additional learning opportunity, relative to young adults.Further research is needed to determine if and how the learning load of a specific pre-sleep memory task influences or moderates subsequent NREM CFC.
Taken together, evidence is accumulating for relations between precise SO -σ CFC and better memory; however, the studies examining this can differ in important ways that merit consideration when synthesising the available data.As this research area continues to develop, it will be important to unify and establish specific taskforce guidelines on CFC measurement to facilitate research standardisation, improve measurement T A B L E 6 Hierarchical regression to predict word-pair consolidation score by SO-sigma MI and CP interaction from Fz on the learning night.N = 25.Note: SO (.5-1.25 Hz); σ, sigma (fixed at 9-13 Hz for Fz).MI, modulation index; CP, absolute coupling phase distance from the SO up-state.F-statistic, p-value, ΔR 2 , B (SE), β and p(β) are from hierarchical regression models to predict word-pair consolidation (Model 2) with centred MI and CP values included alongside a product term reflecting their interaction.Age and apnea-hypopnea index (log-transformed; measured on Night 1) were entered in Model 1. Fstatistic and ΔR 2 are presented only for the final model with interaction term.ΔR 2 , change in proportion of explained variance; SE, standard error.B, unstandardised coefficient.β, standardised coefficient.p(β) is p-value associated with the standardised regression coefficient for the independent variable, controlling for other model predictors.Values in bold denote results that surpassed the conventional critical p-value (< .05).'(base)' refers to the baseline interaction model, containing two mean-centred predictors and their product as an interaction term; models in the two subsequent rows present follow-up analyses to examine moderating effects of MI when a significant interaction was found in the base model (see also Figure 4).Note that regression coefficients for the moderator variable (MI) remain unchanged across each interaction model, whereas the unstandardised and standardised coefficients for CP are recalculated for each model; only the standardised coefficient for the interaction term changes across models.
a Mean-centred main-effect predictor.b Mean-centred moderator values adjusted down by 1 SD unit below the mean (i.e.lower MI).
c Main-centred moderator values adjusted up by 1 SD unit above the mean (i.e. higher MI).
WEINER ET AL.
reliability, and allow for 'meta-analysis-friendly' reports to aide research synthesis.

| SO -σ CFC between baseline and learning nights
SO -σ coupling strength (MI; Tort et al., 2010) and coupling phase distance from the up-state (CP) were both stable on average across the two experimental recording nights, as reflected by a lack of between-night differences, and by sufficient correlations of each measure between nights.The group-level phase-amplitude relationships observed in this study are consistent with previous findings that slower (frontal) spindle/sigma power is more synchronised with the SO up-to-down-state transition (e.g.Helfrich et al., 2019;Klinzing et al., 2016;Muehlroth et al., 2019;Ngo et al., 2013;Yordanova et al., 2017).Our supporting information analyses also show that none of the additional coupling measures (MI, CP, or raw coupling phase, from all SO events or from SO sub-groupings) evidenced a significant difference between nights on either channel.
Together, these results do not support a hypothesis that SO -σ CFC is modulated at the group level by pre-sleep declarative learning, at least for coupling with slow sigma activity in older adults.Although, it is also possible that our learning task was not challenging or demanding enough to influence this type of brain activity to a noticeable degree.
In turn, the current study adds to a mixed literature about relations between coupling strength and sleep-associated memory consolidation.Specifically, although several studies have reported associations between coupling strength and procedural or non-declarative memory (e.g.Bartsch et al., 2019;Hahn et al., 2022;Mikutta et al., 2019), fewer studies have reported positive associations between coupling strength and declarative memory (e.g.Hahn et al., 2020; see also Ladenbauer et al., 2017, andDehnavi et al., 2021), and some others report no association between coupling strength and declarative memory (e.g.Denis et al., 2022;Helfrich et al., 2018;Ladenbauer et al., 2021;Mikutta et al., 2019;Niknazar et al., 2015;Zhang et al., 2020).Conversely, multiple studies have reported that pre-sleep learning and overnight memory consolidation are more reliably associated with measures of SO -σ preferred coupling phase (e.g.Helfrich et al., 2018;Mikutta et al., 2019;Muehlroth et al., 2019;Niknazar et al., 2015;Zhang et al., 2020).
Our results of between-night comparisons are more inline with an alternative hypothesis that, like spindles (Cox et al., 2017;De Gennaro et al., 2005), SO -σ CFC is a stable, trait-like individual difference.Indeed, Cox et al. (2018) demonstrated that SO phase of maximum spindle power/amplitude differed slightly across individuals, between N2 and N3 stages, and between anterior and posterior scalp regions, but remained stable across two consecutive nights.Also, Bastian et al. (2022) recently demonstrated that SO-spindle CFC, in both fast-and slowspindle ranges, did not differ between an experimental night with a pre-sleep spatial memory task versus a nonlearning control recording.Hahn et al. (2022) also showed that SO-spindle coupling strength was highly correlated between an adaptation night and a learning task night.

| SO -σ CFC predicting sleepassociated declarative memory consolidation
Spindle activity is hypothesised to facilitate synaptic long-term potentiation and strengthen newly acquired memory traces (Fernandez & Lüthi, 2020).A recent meta-analysis (Kumral et al., 2022) showed that spindles are associated with both declarative and procedural memory tasks but may in fact have a stronger association with procedural tasks.Emerging research examining F I G U R E 4 Simple slopes reflecting the association between mean-centred CP on Fz (learning night only; x-axis) in predicting word-pair task memory consolidation scores (y-axis) at high, average, and low levels of MI (learning night only).The negative slope reflects the data structure of lower (more negative) CP values signifying a coupling phase distance closer to the SO up-state peak.Coloured ribbons reflect 95% confidence intervals.CP closer to the up-state peak evidenced a stronger predictive association with better memory consolidation when MI values were adjusted higher by 1 SD-unit (β = À.978, p = .001;blue dashed line) compared to MI values adjusted lower by 1 SD unit (β = À.381, p = .120;orange dashed line).The overall model was statistically significant (F (5, 19) = 4.399, ΔR2 = .362,p = .008).Taken together, relations between SO -σ coupling phase closer to the up-state and better memory consolidation may be enhanced when coupling strength is higher and blunted when coupling strength is lower.
NREM CFC suggests that spindle frequency activity, properly timed to the SO up-state, is most optimal for supporting memory consolidation (e.g.Mikutta et al., 2019;Mölle et al., 2009Mölle et al., , 2011;;Niknazar et al., 2015;Ruch et al., 2012).Further, the amplitude of HC ripples (e.g.80-100 Hz) can be modulated by spindle (e.g.12-14 Hz) phase, and both in turn are associated with the SO phase (Amiri et al., 2016;Clemens et al., 2007;Helfrich et al., 2019;Latchoumane et al., 2017;Ngo et al., 2020;Staresina et al., 2015).Evidence is growing for an 'active systems consolidation' model of memory consolidation.This model posits that neural representations (or, engrams) of recently encoded experiences in both neocortical and HC networks are repeatedly coreactivated during NREM sleep, which promotes consolidation across time by reorganising and integrating memory traces from (temporary) HC stores into existing and HC-independent cortical networks; the precise coupling of NREM SOs, spindles and ripples is considered a core neural mechanism of this 'corticalisation' process (e.g.Geva-Sagiv & Nir, 2019;Helfrich et al., 2019;Klinzing et al., 2019;Mölle & Born, 2009;Muehlroth, Rasch, & Werkle-Bergner, 2020;Rasch & Born, 2013).Enhanced CFC may signal a relative increase in functional connectivity during or after a learning period, and perhaps so across domain-specific (e.g.verbal and visual) cortical regions (cf.Yordanova et al., 2017).Importantly, many discussions about SO -σ CFC and memory emphasize the role of this triple SO-spindle-ripple phase-locking in the context of centro-parietal fast spindle activity; conversely, evidence for a potential role of CFC with frontal slow spindle activity in overnight memory consolidation is less consistent.In turn, a principal finding in this study was of an association between coupling phase distance from the up-state with memory consolidation in the context of CFC in the slow spindle range (9-13 Hz) among older adults.
Coupling strength, measured as a relative change score between nights (Primary Results) or examined on each night separately (supporting information Results), was not associated with memory consolidation.Supporting information analyses with rel_MI from SO + spindle events on Cz suggested that a greater increase in coupling strength after learning predicted worse memory.Overall, results from our analyses between coupling strength and memory were generally opposite to expectation.Measures of coupling strength are reported in several studies of CFC and memory, although some (e.g.Niknazar et al., 2015) have proposed that SO -σ coupling phase near the up-state may be a stronger predictor of memory.
Although our measures of raw coupling phase did not correlate with memory in this study (supporting information Results), our transformed variable of coupling phase distance from the SO up-state (CP) did.Specifically, primary analyses with rel_CP (N2 + N3, Fz) suggested that older individuals whose SO -σ coupling phase shifted towards the SO up-state consolidated more word-pair associations relative to those whose CP shifted further away from the up-state.A similar association was found in our supporting information analyses with rel_CP from isolated SO events not joined with a spindle (SO(À) -σ, N2 + N3, Fz).However, the same effect was not observed with SO + spindle events or with any CP measure from Cz (supporting information Results).The lack of results from our Cz channel could be because of the limited variability in CP on Cz within and between nights, relative to Fz, or because of the skewed distributional qualities of measures from Cz. Collectively, these results support an argument that potentially important distinctions in coupling dynamics likely exist when measures are derived from isolated versus naturally co-occurring events, or from all SO events.SOs and spindles are distinct oscillatory events that can appear in isolation but are also known to spontaneously co-occur (Hahn et al., 2020;Oyanedel et al., 2020;Schreiner et al., 2021).Studies that examined SO -σ CFC in the context of co-occurring SO-spindle complexes in humans (e.g.Hahn et al., 2020;Helfrich et al., 2019;Klinzing et al., 2016;Muehlroth et al., 2019;Niknazar et al., 2015;Schreiner et al., 2021) and rats (e.g.Oyanedel et al., 2020) highlight the potential importance of leveraging the natural co-occurrence of neural oscillations when studying measures of CFC.For instance, Oyanedel et al. (2020) showed that ripple (150-250 Hz) power enhancement around the SO up-state was strongest among SO events that co-occurred with a spindle versus isolated SOs, and that power suppression during the SO downstate was strongest among isolated SOs.To our knowledge, there is a paucity of studies that examine CFC among SO-spindle complexes in older adults and in the context of memory, and of studies drawing comparisons between CFC measures derived between SO(+) and SO(À) events in this age group.The difference in outcome between SO sub-groups (e.g.relatively greater amplitude modulation on SO[+] events) also highlights that sigma spectral power is a proxy of spindle activity, and that sigma power dynamics may differ when in the presence or absence of a detectible spindle event.Such differences may have unique functional properties, signal-processing considerations and associations with memory.
Together, our study with healthy older adults suggests that a slow spindle coupling phase closer to the SO upstate is predictive of better memory, but only on the frontal channel, and only in the context of a combined N2 + N3 sleep period.This finding is intriguing given the emphasis that has been placed on memory-related benefits of SO-coupling with fast (relative to slow) spindle power in previous studies, mainly with young adults (e.g.Helfrich et al., 2018;Mölle et al., 2011;Muehlroth et al., 2019).Our main analyses yielded statistically significant associations between CP (measured from Fz) and memory during a combined N2 + N3 sleep stage, whereas our supporting information analyses with each stage examined separately did not yield similar results.The dynamics and properties of SOs and spindles may differ across the two NREM stages (N2 and N3).For example, the extent or magnitude of spindle power synchronising to the SO phase could differ between lighter and deeper NREM sleep (cf.Cox et al., 2018), which may have resulted in weaker associations with memory in this sample when stages were examined separately.Alternatively, perhaps there was not enough statistical power to detect an effect using data from each stage separately, compared to using data from the combined sleep stage; this speaks to the need for replicating our analyses with a larger sample.Results with relative change in CFC further suggest that individual-level differences in coupling dynamics may be an important factor to consider when examining SO -σ CFC and memory (e.g.differences in brain activity profiles between participants whose coupling phase shifted towards, versus away from, the upstate after learning), and this variability may be especially relevant in research with older adults.
Two recent studies of SO -σ CFC during overnight sleep (Helfrich et al., 2018;Muehlroth et al., 2019) provide evidence that less precise timing of SO and spindle activity with ageing is associated with reduced grey matter volume in the medial pre-frontal cortex and with worse declarative memory performance.Although both studies examined fast spindle power on central EEG channels, Muehlroth et al. (2019) also examined coupling with slow spindle power on frontal (F3 and F4) channels.Muehlroth and colleagues described that a 'youth-like' SO-fast spindle coupling pattern, with a peak at or just after the up-state, is associated with better memory retention, and greater medial-pre-frontal and thalamic grey volume; the older adults with a 'youthlike' coupling pattern did better on memory testing, whereas older (and younger) adults with a more 'aged' pattern (fast spindle activity peaking too early before the up-state, stronger slow spindle power increases between the up-state and down-state) showed worse memory.Muehlroth et al. (2019) suggest that slow spindles may not be effective in HC-dependent memory consolidation and may be more reflective of cortico-cortical communication rather than HC-thalamic-cortical communication.Slower spindle power (from Fz) in our study tended to peak after the up-state, during the up-to-down-state transition, and faster spindle power (from Cz; supporting information Results) tended to peak before or during the up-state, which is consistent with previous reports (e.g.Mölle et al., 2011;Muehlroth et al., 2019).However, inspection of our data showed that this was not true for everyone, as two participants' coupling phase was locked before the up-state on Fz, and one participant's coupling phase was locked after the up-state on Cz.Our finding of rel_CP shift towards the up-state on Fz and better memory could reflect the more 'youth-like' properties of these individuals' brain activity, relative to those whose CP shifted away from the up-state.Examining this further would be aided by a study with samples of 'younger' older and 'older' older adults, alongside a young adult control group.
In considering that measures of coupling strength and coupling phase are reflections of the same underlying construct, we also conducted an exploratory analysis to examine potential interaction effects between SO -σ MI and CP in predicting memory consolidation.A regression model containing the mean-centred MI, CP and MI Â CP interaction variables significantly predicted word-pair overnight consolidation scores in our sample of healthy older adults.Follow-up moderation analyses suggested that the association between coupling phase closer to the up-state and memory consolidation was enhanced when coupling strength was higher and diminished when coupling strength was lower.Again, this effect was found only with slower spindle activity from Fz and was not seen with faster spindle activity from Cz (supporting information Results).This may be interpreted as indicating that the memory-enhancing effect of SO -σ coupling strength is contingent on the timing of spindle activity with respect to the SO; stated differently, greater coupling strength alongside poorly timed spindle power increases may merely result in stronger 'bad' coupling, which may impede HC-neocortical transactions.These interaction effects should be interpreted cautiously given our small sample size, but the results provide an interesting perspective about interpreting the functional significance of one type of coupling measure (e.g.coupling phase) in the context of the other (e.g.coupling strength), rather than separately.Relatedly, Ohki (2022) has recently described a novel measure that considers both amplitude and phase position data in examining phase-amplitude coupling.Given the significant memory associations with our coupling phase distance variable and its interaction with coupling strength, we provide evidence that the two measures may have unique functional contributions to memory.It would be interesting if any interacting effects on memory between MI and CP change across the lifespan; however, testing this would require a larger sample and a young adult control group.

| SO -σ CFC and lifespan ageing
An important contemporary research topic is of examining age-related declines in CFC, and how this could account for memory impairments with ageing.Most available studies examining CFC during sleep, in or outside the context of memory, report on data from young adults.Both SO and spindle activity decline with older age (e.g.Carrier et al., 2011;Martin et al., 2013), and some evidence suggest the same is true for SO -σ CFC.In the context of development, SO -σ CFC was shown to increase from childhood to adolescence across a 7-year follow-up (Hahn et al., 2020).However, similar longitudinal research is lacking in the context of ageing.Ageingrelated frontal and thalamic deterioration and impaired SO-triggered spindles are two mechanistic explanations for SO -σ 'de-coupling' seen with ageing (e.g.fast spindle activity peaking out of time with the SO up-state in older versus younger adults; Helfrich et al., 2018;Muehlroth et al., 2019).Disrupted TC network integrity with older age could also impair NREM coupling and, in turn, sleep-dependent memory consolidation.
The present study did not have a young adult comparison group, and thus could not examine age-group differences in CFC.Nevertheless, findings show that SO -σ coupling phase distance closer to the up-state is positively associated with memory in older adults, suggesting that coupled brain activity continues to facilitate sleepassociated memory processes in older age.However, this requires more investigation in studies directly comparing younger and older adults.Further, cross-sectional comparisons between younger and older groups can only provide so much information about age-related changes or declines in coupling strength and coupling phase.A prospective longitudinal design is needed to study long-term changes in both coupling measures and their relations with memory.
Our results must also be interpreted considering the analytical decisions made, and in relation to what is known about NREM oscillations and ageing.Chiefly, one of the primary components in measuring SO -σ CFC is the data derived from detected SO events.Our SO detector was based on Staresina et al. (2015) and utilised an adapted amplitude thresholding procedure applied to candidate SOs that met other criteria.In turn, this detection finds the largest slow waves for each participant and recording, which is optimal considering the reduced amplitude of slow waves often seen in seniors (cf.Webb & Dreblow, 1982).This can be compared with other slow wave detection methods with a fixed amplitude threshold (e.g.peak-to-peak amplitude ≥ 140 μV; Massimini et al., 2004).However, based on recent research in animals (Kim et al., 2019), there may be functional differences in oscillation activity between SO (e.g.< 1 Hz) and delta (e.g.1-4 Hz) bands in relation to memory (i.e.facilitating retention vs. forgetting).Accordingly, it is important to consider the difference in numbers and characteristics of SOs found among different detectors.Together, these points about SO detection echo conclusions from recent reviews (Muehlroth, Rasch, & Werkle-Bergner, 2020; Muehlroth & Werkle-Bergner, 2020) that stressed the importance of designing 'age-fair' studies when examining ageing.Changes with age in oscillation activity (e.g.reduced amplitude or frequency) should not be ignored in studies that include data from older adults.

| Study limitations and strengths
There are several limitations of this study that merit consideration.First, while this study examined relative change in CFC between a learning night and a nonlearning baseline, the baseline was also the first screening night.It is possible that this first recording visit was suboptimal as a baseline because, for most participants, this was their first experience in a sleep lab and with the recording equipment (i.e.new sights, sounds and sensations).In turn, it is possible that the lack of differences in CFC measures between nights could also be explained by the added 'learning' involved on the (first) PSG night.Sleep architecture was largely similar on both nights; however, the participants achieved better sleep efficiency on Night 2 (average SE% = 83.26% vs. 85.71%).Thus, we cannot rule out the influence of a possible first-night effect without a study that includes at least three recording nights.It remains to be established if sleep microarchitecture (including CFC) is susceptible to first-night effects like sleep macro-architecture.Importantly, our supporting information analyses demonstrated that the association between CP and memory was specific to the second (learning task) night, whereas there was no association found between CP and memory on the first night.There were no differences in our main CFC variables or our secondary variables (detected events and PSD) between nights, except that spindle peak-to-peak amplitude decreased on the second (learning) night.Although we can only speculate about why spindle amplitude alone was greater on Night 1, it is possible that this reflects a learning effect from the overall novelty of participants' first recording visit (e.g.sleeping in our lab, experiencing the equipment set-up and receiving instructions for athome sleep monitoring).Alternatively, greater spindle amplitude on the first visit could reflect a relative enhancement of underlying TC network activity associated with extra sensory gating in response to the novel sleep lab experience (e.g.unfamiliar bedroom and wearing the recording equipment while sleeping; Fernandez & Lüthi, 2020;Schabus et al., 2012).Second, and relatedly, our baseline night did not include any control task.A control task that requires similar cognitive engagement would provide a more refined test of how learning might influence coupling dynamics.Third, our sample may have been underpowered and included participants with a range of sleep apnea severity.Although this may help enhance our study's generalisability, and our analyses included AHI as a covariate, the deleterious effects of sleep apnea on sleep continuity and stability could have introduced extraneous variance and impeded some subjects from achieving deep enough sleep for optimal slow wave activity to occur (e.g. higher sleep fragmentation).Our research team is currently completing data collection for a follow-up study that addresses each of these limitations, by including three recording nights, a cognitive control task and stricter limits for sleep apnea severity, as well as a young adult control sample to examine agegroup differences.
Aside from these limitations, this study has noted strengths.First, the participants were recruited and selected using stringent a priori criteria that required them to satisfy thresholds on screening tests of cognitive functioning, and across a battery of self-report questionnaires.Second, the word pairs selected for the memory task were carefully chosen and constructed using specific criteria about word length and frequency, and considering the emotionality of included words.It is also important to note that our word-pair associates task used a cued-recall test, which is different from earlier and oftencited studies of NREM CFC and memory in older adults (Helfrich et al., 2018;Ladenbauer et al., 2017;Muehlroth et al., 2019) that placed more emphasis on tests of recognition memory.Third, CFC was computed using data from both nights of sleep, allowing for an examination of relative change in CFC after learning.Fourth, our analysis methods are in-line with current recommendations for deriving measures of CFC (e.g.computing CFC measures from detected oscillatory events; cf.Aru et al., 2015).Finally, and overall, this study capitalised on available data by providing a comprehensive analysis of coupling dynamics during NREM sleep in our sample of healthy older adults.

| CONCLUSION
Results of our study with older adults suggest that measures of SO -σ coupling strength and coupling phase do not reliably change between a baseline and a learning condition, but that memory consolidation may be facilitated by a shift in coupling phase towards the SO up-state.Moreover, our exploratory interaction model revealed, to our knowledge, a novel finding that the strength of association between coupling phase closer to the up-state and better memory may be enhanced when accompanied by greater (vs.weaker) coupling strength.This study builds on and extends previous work by (1) examining SO -σ CFC after a pre-sleep learning task, and as a measure of relative change from a non-learning baseline; (2) examining associations with memory using a transformed measure of coupling phase distance from the up-state; and (3) examining the interactive effects between SO -σ coupling strength and coupling phase distance.
Note: SO (.5-1.25 Hz); σ, sigma (fixed at 9-13 Hz).rel_MI, change in modulation index between nights.rel_CP, change in absolute coupling phase distance from the SO up-state between nights.F-statistic, p-value, ΔR 2 , B (SE), β and p(β) are from hierarchical regression models with the coupling measure of interest as the independent variable predicting word-pair consolidation in Model 2. Age and apnea-hypopnea index (log-transformed; measured on Night 1) were entered in Model 1. p(β) is p-value associated with the standardised regression coefficient for the independent variable, controlling for other model predictors.Values in bold denote results that reached or surpassed Bonferroni-adjusted p-value (.013).B, unstandardised coefficient.β, standardised coefficient; ΔR 2 , change in proportion of explained variance; SE, standard error.a N = 23, two participants removed as outliers prior to analysis with rel_MI on Fz.F I G U R E 3 (a) Scatterplot displaying association of word-pair memory consolidation score (on y-axis) with relative change in SO -σ MI between nights from Fz (rel_MI; x-axis).Values of rel_MI above zero reflect greater coupling strength on the learning night.(b) Scatterplot displaying association of word-pair memory consolidation score (on y-axis) with relative change in SO -σ CP between nights from Fz (rel_CP; x-axis).Negative associations (and negative beta value) correspond with the data structure of negative values on this relative CP variable reflecting a shift closer to (vs.further from) the SO up-state after learning compared to baseline; a greater shift towards the up-state after learning predictied better memory consolidation.Standardised coefficient and p-value on each plot is from hierarchical regression models examining rel_MI or rel_CP in predicting word-pair memory performance, controlling for age and sleep apnea severity.
Specific aim 1: SO -σ CFC during sleep after learning in healthy older adults Presented in Table 4 are descriptive statistics and betweennight comparisons for coupling strength (MI) and coupling phase distance from the up-state (CP).Coupling dynamics across study nights are depicted in Figure 2. CouplingT A B L E 1 Demographics and screening.N = 25.
T A B L E 2 Note:T A B L E 3 Note: M, mean; SD, standard deviation.Freq, frequency.sec, seconds; μV; microvolts; Hz, Hertz.Negative t-values indicate a larger value on Learning (Night 2) visit.Pearson's correlations revealed highly stable values for each measure from the first to second overnight recording (SOs: all r > .614,all p ≤ .001;Spindles: all r > .814,all p < .001).
Descriptive statistics and between-night comparison of SO-sigma MI and CP from Fz. N = 25.SO, slow oscillation (.5-1.25 Hz); σ, sigma (fixed at 9-13 Hz).MI, modulation index.CP, absolute coupling phase distance from the SO up-state.M, mean; SD, standard deviation, med, median.F-statistic, p-value, and Partial η 2 are for repeated-measures ANCOVA with Night (1/baseline vs. 2/learning) as the Note: repeated-measures factor.Age and apnea-hypopnea index (log-transformed; measured on Night 1) were included as covariates.Pearson's correlations revealed highly stable values for each measure from the first to second overnight recording (MI: r = .732,p < .001;CP: r = .669,p < .001),but no significant relationship between MI and CP on either night (r-range: À.136-.140,all p > .504).
T A B L E 5 Hierarchical regression to predict word-pair consolidation score by SO-sigma rel_MI and rel_CP from Fz. N = 25.